Problem: Solve for $w$. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. $53w+13 < 56w + 16$
$\begin{aligned}53w+13 & < 56w + 16 \\\\ 53w&< 56w+3 &(\text{Subtract } 13 \text{ from both sides}) \\\\ -3w &< 3 &(\text{Subtract } 56w \text{ from both sides})\\\\ 3w&> -3&(\text{Multiply both sides by }-1)\\\\ w&>-1&(\text{Divide both sides by }3 \text{ and simplify}) \end{aligned}$ [Why did the inequality sign flip when we multiplied by -1?] In conclusion, the answer is $w >-1$.